Donald Trump handed the German chancellor Angela Merkel a bill — thought to be for more than £300bn — for money her country “owed” Nato for defending it when they met last weekend, German government sources have revealed.

The bill — handed over during private talks in Washington — was described as “outrageous” by one German minister.

Officials calculated the extent to which German defence spending had fallen short of the 2% target each year, added the amount together — and then put interest on top.

“The concept behind putting out such demands is to intimidate the other side, but the chancellor took it calmly and will not respond to such provocations,” the minister said.

Trump has criticised a number of Nato countries — Germany among them — for insufficient military spending, leaving America to pick up more than its fair share of the tab. He wants them to honour a commitment made in 2014 to invest 2% of their GDP in defence — a target met at present only by the US, Britain, Estonia, Greece and Poland.

Trump appeared to go one step further during his meeting with Merkel. Taking 2002 as a starting point, his officials calculated the extent to which German defence spending had fallen short of the 2% target each year, added the amount together — and then put interest on top.

US officials told their German counterparts they chose 2002 because, they claim, that was the year Merkel’s predecessor, Gerhard Schröder, committed his country to higher defence spending.

Neither side revealed the total, though official figures suggest a cumulative shortfall of more than £250bn. Addition of compound interest would take the amount past £300bn. According to diplomatic sources, Trump had his staff prepare similar calculations for all other Nato members below the 2% target.

A source close to Merkel was dismissive. “The president has a very unorthodox view on Nato defence spending,” the source said. “The alliance is not a club with a membership fee. The commitments relate to countries’ investment in their defence budgets.”

Merkel is said to have “ignored the provocation”, but did commit to raise German defence spending gradually, although she asked for spending on international development to be taken into consideration.